1. Insight Through Computing 13. More on Arrays Square Bracket Notation Subscripts Plotting and color Built-In Functions: ginput, fill, sum, axis

2. Insight Through Computing The Square Bracket These are equivalent: x = linspace(0,1,5) x = [ 0.25.50.75 1.00] 0.00 0.25 0.50 0.75 1.00 x: Handy for setting up “short” vectors.

3. Insight Through Computing Three “Short Vector” Examples Line Segments Little Polygons Color

4. Insight Through Computing Plotting a Line Segment a = 1; b = 2; c = 3; d = 4; plot([a c],[b d]) This draws a line segment that connects (1,2) and (3,4): A natural mistake: plot([a b],[c d])

5. Insight Through Computing Drawing Little Polygons x = [a a+L a+L a a]; y = [b b b+W b+W b]; plot(x,y) This draws an L-by-W rectangle with lower left corner at (a,b): Connect (a,b) to (a+L,b) to (a+L,b+W) to (a,b+W) to (a,b)

6. Insight Through Computing Coloring Little Polygons x = [a a+L a+L a a]; y = [b b b+W b+W b]; fill(x,y,c) This draws an L-by-W rectangle with lower left corner at (a,b) and colors with the color named by c: Connect (a,b) to (a+L,b) to (a+L,b+W) to (a,b+W) to (a,b) and then fill it in.

7. Insight Through Computing Built-In Function Fill fill(,, ) Vectors that specify the vertices of a polygon. Specify the fill-in color.

8. Insight Through Computing x = [0.11 -0.99 -0.78 0.95] y = [0.99 0.08 -0.62 -0.30] fill(x,y,’y’)

9. Insight Through Computing DrawRect function DrawRect(a,b,L,W,c) x = [a a+L a+L a a]; y = [b b b+W b+W b]; fill(x,y,c)

10. Insight Through Computing Color is a 3-vector Any color is a mix of red, green, and blue. Represent a color with a length-3 vector and an “rgb convention”. c = [ 0.25 0.63 0.00 ] red value between 0 and 1 blue value between 0 and 1 green value between 0 and 1

11. Insight Through Computing Some Favorites White[0 0 0] Blue[0 0 1] Green[0 1 0] Cyan [0 1 1] Red[1 0 0] Magenta[1 0 1] Yellow[1 1 0] Black[1 1 1]

12. Insight Through Computing A Problem Display all colors [r g b] where r ranges over the values 0.00 0.25 0.50 0.75 1.00 g ranges over the values 0.00 0.25 0.50 0.75 1.00 b ranges over the values 0.00 0.25 0.50 0.75 1.00

13. Insight Through Computing Preliminary Notes There will be 5 x 5 x 5 = 125 colors to display. To display a color, we will draw a unit square with that color.

14. Insight Through Computing Script Derivation for r = 0:.25:1 Display all colors with red value r. end Refine This!

15. Insight Through Computing Script Derivation for r = 0:.25:1 for g = 0:.25:1 Display all colors with red value r and green value g. end Refine This!

16. Insight Through Computing Script Derivation for r = 0:.25:1 for g = 0:.25:1 for b = 0:.25:1 Display the color with red value r, green value g, and blue value b. end Refine This!

17. Insight Through Computing Script Derivation for r = 0:.25:1 for g = 0:.25:1 for b = 0:.25:1 c = [r g b]; fill(x,y,c) end Done!

18. Insight Through Computing Subscripts It is possible to access and change specific entries in an array. x = [ 0.25.50.75 1.00] The value of x(1) is 0.00. The value of x(2) is 0.25. The value of x(3) is 0.50. The value of x(4) is 0.75. The value of x(5) is 1.00. 0.00 0.25 0.50 0.75 1.00 x:

19. Insight Through Computing Subscripts It is possible to access and change specific entries in an array. x = [ 0.25.50.75 1.00] 0.00 0.25 0.50 0.75 1.00 x: a = x(1) a = x(2) a = x(3) a = x(4) a = x(5) 0.00 0.25 0.50 0.75 1.00

20. Insight Through Computing Subscripts It is possible to access and change specific entries in an array. x = [ 0.25.50.75 1.00] 0.00 0.25 0.50 0.75 1.00 x: for k = 1:5 a = x(k) end 0.00 0.25 0.50 0.75 1.00

21. Insight Through Computing Subscripts It is possible to access and change specific entries in an array. x = [ 0.25.50.75 1.00] 0.00 0.25 0.50 0.75 1.00 x: a = x(1)+x(2) a = x(2)+x(3) a = x(3)+x(4) a = x(4)+x(5) 0.25 0.75 1.25 1.75

22. Insight Through Computing Subscripts It is possible to access and change specific entries in an array. x = [ 0.25.50.75 1.00] 0.00 0.25 0.50 0.75 1.00 x: for k=1:4 a = x(k)+x(k+1) end 0.25 0.75 1.25 1.75

23. Insight Through Computing Subscripts This x = linspace(a,b,n) is equivalent to this h = (b-a)/(n-1); for k=1:n x(k) = a + (k-1)*h; end

24. Insight Through Computing Subscripts h = (1-0)/(5-1); x(1) = 0 + 0*h; x(2) = 0 + 1*h; x(3) = 0 + 2*h; x(4) = 0 + 3*h; x(5) = 0 + 4*h; 0.00 0.25 0.50 0.75 1.00 x:

25. Insight Through Computing Subscripts h = (b-a)/(n-1); for k=1:n x(k) = a + (k-1)*h ; end Recipe for a value Where to put it.* * Only now we compute where to put it. x(k)a + (k-1)*h

26. Insight Through Computing A Problem Click in the three vertices of a triangle. Display the triangle. Compute the centroid (xc,yc). Highlight the centroid and the vertices. Connect each vertex to the centroid.

27. Insight Through Computing Clicking in the Vertices The command [x,y] = ginput(3) will assign the xy coordinates of the clicks to the arrays x and y. Clicks: (1,2), (3,4), (5,6) x: y: 1 3 5 2 4 6

28. Insight Through Computing Display the Triangle fill(x,y,’y’)

29. Insight Through Computing Compute the Centroid xc = (x(1) + x(2) + x(3))/3; yc = (x(1) + y(2) + y(3))/3; The x coordinate of the centroid is the average of the x-coordinates of the vertices. Ditto for y-coordinate.

30. Insight Through Computing Highlight the Vertices and Centroid plot(x,y,’ok’,xc,yc,’*k’)

31. Insight Through Computing Connect Each Vertex to the Centroid plot([xc x(1)],[yc y(1)]) plot([xc x(2)],[yc y(2)]) plot([xc x(3)],[yc y(3)])

32. Insight Through Computing Overall [x,y] = ginput(3) fill(x,y,’y’) xc = (x(1)+x(2)+x(3))/3; yc = (y(1)+y(2)+y(3))/3; plot(x,y,’ok’,xc,yc,’*k’) plot([xc x(1)],[yc y(1)]) plot([xc x(2)],[yc y(2)]) plot([xc x(3)],[yc y(3)])

33. Insight Through Computing More General n = 3; [x,y] = ginput(n) fill(x,y,’y’) xc = sum(x)/n; yc = sum(y)/n; plot(x,y,’ok’,xc,yc,’*k’) for k=1:n plot([xc x(k)],[yc y(k)]) end

34. Insight Through Computing Question Time What is the output? x = [10 20 30]; y = [3 1 2] k = y(3)-1; z = x(k+1) A. 11 B. 20 C. 21 D. 30 E. 31

35. Insight Through Computing A Problem Plot the function y = sin(x) across [0,2pi] but add random noise if In particular, use sin(x)+.1*randn(1) if x is in this range.

36. Insight Through Computing Solution x = linspace(0,2*pi,n); y = sin(x); for k=1:n if 2*pi/3 <= x(k) && x(k) <= 4*pi/3 y(k) = y(k) +.1*randn(1); end plot(x,y) axis([0 2*pi -1.2 1.2 ]) x range:[0 2pi] y range: [-1.2 1.2]

37. Insight Through Computing

38. Problem On a black background, click in the location of 10 stars. (A “constellation”.) Repeat many times: for k=1:10 Redraw the k-th star using black or yellow with equal probability end This box redraws the constellation.

39. Insight Through Computing To Simulate Twinkling… [x,y] = ginput(10); for k = 1:100 for j=1:10 if rand <.5 DrawStar(x(j),y(j),r,'k') else DrawStar(x(j),y(j),r,'y') end pause(.01) end

40. Insight Through Computing Subscripting Review for j=1:3 DrawStar(a(j),b(j),.1,’y’) end DrawStar(3,2,.1,’y’) a:a: b: 13 482 7 j=1

41. Insight Through Computing Subscripting Review for j=1:3 DrawStar(a(j),b(j),.1,’y’) end DrawStar(1,8,.1,’y’) a:a: b: 13 482 7 j=2

42. Insight Through Computing Subscripting Review for j=1:3 DrawStar(a(j),b(j),.1,’y’) end DrawStar(7,4,.1,’y’) a:a: b: 13 482 7 j=3